Oscillations and Concentrations in Compressible and Incompressible Fluids
Final rept. 1 Jan 1989-31 Dec 1991
CALIFORNIA UNIV BERKELEY
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A fast vortex method was developed for solving the incompressible Euler equations in three dimensions. It is based on a combination of Andersons Method of Local Corrections, which uses a hybrid of a finite difference representation and a particle representation to compute the velocity field induced on the vortices, and of adaptive mesh refinement for the finite difference calculation, The resulting algorithm is faster than any other existing finite difference or multipole - based algorithm for this problem and is 10-20 times faster than the direct N-body method for problems of current research interest. In addition, a good deal of technology was developed for finite-difference Poisson solvers of independent interest and usefulness, such as a multigrid-based local refinement algorithm for Mehrstellen discretizations of Poissons equation in three dimensions, and efficient treatment of boundary conditions for boundaries that have infinite extent in one or more of the coordinate directions.
- Theoretical Mathematics
- Fluid Mechanics